Question

What does it mean for a number to be the "solution" to an equation?

Give an example of a variable equation and its solution.
Explain in complete sentences how you know that number is the solution

Answer 1

Basically, in order for a number to be the "solution" to an equation, the equation can only be true if the variable is equal to that number. If you were to substitute a different number for the variable in the equation, then the two sides of the equation would not be equal.

If you were given the equation:

2(x + 7) = 18

then the only way on earth for the two sides for the equation to be equal (the left side equals the right side) is if the variable "x" were 2. If you were to substitute 2 for x, then the equation would be true, and if you were to substitute any other number, the equation would be false.
So 2 is the ONLY number that could replace "x" and keep the equation true, therefore 2 is the solution to this equation.

Sometime more than one number could be solutions to an equation (so there doesn't always have to be only one solution).

Answer 2

A number to be a solution means that number is satisfying the equation which means making left hand side equal to right hand side.
Example x-1=0
here x=1 is a solution of the equation x-1
when we put x=1
1-1=0
so Left hand side = right hand side.
Hence x=1 is the solution

Answer 3

if a number/integer/value satisfies the equation, then it is a solution to an equation/problem...

eg.
1. 5x - 10 = 25 ; x=7, ergo 7 is a solution to the equation
2. find all numbers that would satisfy x - 5 > 0... the solution/solution SET for this is all real numbers >= 6...